To allow for a robust and adaptive PAD system, we extend the standard one-shot training/testing formulation of PAD to a continual learning setting [1]}.
To this end, we consider that after the initial training phase, PAD tasks arrive sequentially and we need to address these tasks at inference time. We consider that the system encounters
sequential PAD tasks \(\lbrace \mathcal {Z}^{t}\rbrace _{t=1}^{T_{\text{Max}}}\)  in a time sequence \(t=1, \ldots , T_{\text{Max}}\)  during execution time. Each task is specified by an unlabeled training dataset \(\mathcal {D}^{t} = \langle \mathbf {X}^{t}\rangle \) , \(\mathbf {X}^{t}\in \mathbb {R}^{d\times n_t}\) , built from observed input data points over a fixed time period, e.g., a day. The unlabeled dataset for subsequent tasks may contain new attack types that were not present when the previous tasks were learned, i.e., the tasks may have different distributions \( q^{t}(\mathbf {x})\) . This means that we need to equip the PAD module with a mechanism such that the system can identify instances of unknown types of attacks in the dataset \(\mathcal {D}^{t}\)  at each time-step \(t\)  and then update the model to learn them (see Figure REF ).
